Bayesian Classification: Asymptotic Results

We have a population composed of two subpopulations whose probability properties are described by known univariate distribution functions, $G(x)$ and $H(x)$, respectively. The probability of observing an individual from the first population is θ, from the second is 1 - θ. We assume θ is a random variable with a prior distribution on (0, 1) and find the Bayes rule for classifying n observations as from G or from H when the loss function is equal to the number of misclassifications. The main results in the paper give the asymptotic properties of the Bayes rule and several proposed approximations.